According to [1] an n-dimensional N–set is a compact subset A of Rn such that for every x ∈ Rn there is y ∈ A with y − x ∈ Zn. We prove that every two dimensional N–set A must contain distinct points x, y such that x − y is in Z2 and x − y is neither horizontal nor vertical. This answers a question of P. Hegarty and M. Nathanson. For any sets A,B in an abelian group A±B denotes the set {a±b : a...

Theorem. If fo is a continuous function on a compact set C without interior and with connected complement of the complex plane, and if fi, • • ■ i fn are continuous functions on a compact totally disconnected subset E of C, then there exists a sequence {pi} of polynomials such that pi-^fo uniformly on C as i—* , and pim—*fk uniformly on E as i—>», for lslk^n, where pi[k] is the kth derivativ...

This paper develops several aspects of shift-invariant spaces on locally compact abelian groups. For a second countable locally compact abelian group G we prove a useful Hilbert space isomorphism, introduce range functions and give a characterization of shift-invariant subspaces of L 2 (G) in terms of range functions. Utilizing these functions, we generalize characterizations of frames and Ries...

I present an algorithm that, given a number $n \geq 1$, computes a compact representation of the set of all noncrossing acyclic digraphs with $n$ nodes. This compact representation can be used as the basis for a wide range of dynamic programming algorithms on these graphs. As an illustration, along with this note I am releasing the implementation of an algorithm for counting the number of noncr...

In a previous paper [4] we obtained the Hopf algebra structure of k*(G ; Q(P» where G is a compact connectvd Lie group and Q(P) is the quotient ring of Z with respect to a multiplicative subset generated by a set of primes, such that H*(G ; Q(P)) is torsion free . Here we study the properties of the connective K-theory of the Lie groups Spin(n) . Since H*(Spin(n) ; Z) is torsion free if n _< 6,...

We study holomorphic foliations of codimension $k\geq 1$ on a complex manifold $X$ dimension $n+k$ from the point view exceptional minimal set conjecture. For $n\geq 2$ we show in particular that if normal bundle $N_{\mathcal{F}}$ is Griffiths positive, then foliation does not admit compact invariant complete intersection $k$ smooth real hypersurfaces $X$.

Let (M, g) be a simply connected complete Kähler manifold with nonpositive sectional curvature. Assume that g has constant negative holomorphic sectional curvature outside a compact set. We prove that M is then biholomorphic to the unit ball in Cn, where dimCM = n. Résumé. Soit (M, g) une variété kählérienne complète et simplement connexe à courbure sectionnelle non-positive. Supposons que g ai...